Originally Posted by

**Mr.Ree** Hello. I am new to this forum, and starting a new topic in calculus. I need some help with integration to find areas under certain curves (see picture).

I worked out the two trig functions to be:

1) cos ((pi*x)/2)]

because: positive cosine function

Amplitude = 1

Period = 4 = [2*pi]/B

-> B = 2*pi/4

-> B = pi/2

2) -cos ((pi*x)/2)

because: negative cosine function

Amplitude = 1

Period = 4 = [2*pi]/B

-> B = 2*pi/4

-> B = pi/2

How do I integrate and find the areas under these graphs?

The other 4 functions which look like exponentials I need some help with:

I want to use: y = A*e^(kx) and manipulations of that, but I am wondering whether substituting my points will work because I have no initial value since y intercept is not given. How can I find the equations of the exponential functions from just the graph. (I'd love to learn how without a calculator)